Problem 56 - College Algebra with Corequisite Support

Question

Use this data for the exercises that follow: In \(2013,\) there were roughly 317 million citizens in the United States, and about 40 million were elderly (aged 65 and over). \(^{2}\) If you meet a U.S. citizen, what is the percent chance that the person is elderly? (Round to the nearest tenth of a percent.)

Step-by-Step Solution

Answer

12.6%

Step 1: Understand the Problem

We need to find the percent chance that a randomly selected U.S. citizen is elderly, given that there are 317 million total citizens and 40 million elderly citizens.

Step 2: Determine the Fraction

The fraction representing elderly citizens over the total population is given by dividing the number of elderly citizens by the total population: \( \frac{40 \text{ million}}{317 \text{ million}} \).

Step 3: Calculate the Decimal

Convert the fraction to a decimal: \( \frac{40}{317} \approx 0.1261 \). This represents the probability in decimal form.

Step 4: Convert to Percentage

To find the percentage, multiply the decimal by 100: \(0.1261 \times 100 = 12.61\).

Step 5: Round the Percentage

Round 12.61 to the nearest tenth of a percent, which gives us 12.6%.

Key Concepts

Percentage

A percentage is a way to express a number as a fraction of 100. It is a useful tool to compare proportions because it standardizes numbers into a uniform format. In everyday contexts, percentages can represent items like tax rates, discounts, or population statistics. For example, if you want to know how much of a population is elderly, you might express this as a percentage. In our exercise, we converted a fraction into a percentage to easily compare the proportion of elderly citizens against the total population. This helps provide a clear understanding of how significant a portion of the population is elderly.

Fraction to Decimal Conversion

Converting fractions into decimals is a fundamental math skill. It involves dividing the numerator (top number) by the denominator (bottom number). This process gives you a decimal equivalent which can be more intuitive to work with for some calculations.
For instance, in our exercise, we converted the fraction of elderly citizens over the total population (40 million divided by 317 million) into a decimal (approximately 0.1261). This decimal helps in calculating the percentage later on and in understanding the data more clearly.

Population Statistics

Population statistics involve analyzing data to understand characteristics within a population. These statistics can include age distribution, gender, or other demographic factors. They help shape policies and business decisions by providing insight into a population's needs.
In our exercise, understanding the elderly population within the U.S. involves population statistics. We calculated the percentage of citizens aged 65 and over to see how this group compares to the rest. This analysis is essential for planning resources like healthcare, retirement programs, and community services targeted at elderly individuals.

Elderly Population Analysis

Elderly population analysis is an important aspect of demography. It focuses on understanding the distribution and needs of senior citizens within a community.
By analyzing this group, governments can tailor services such as healthcare, retirement benefits, and social programs to better serve these individuals. In our exercise, calculating the percentage of elderly citizens in the U.S. offers insight into how large this segment is relative to the entire population. Such analyses are vital for developing strategies to support the well-being and integration of the elderly into society.